asymmetry in the Higgs boson decay into a top quark pair due to top squark mixing

PHYSICAL REVIEW D, VOLUME 64, 015010

CP asymmetry in the Higgs boson decay into a top quark pair due to top squark mixing

Fred BrowningPhysics Department, University of Illinois at Chicago, Chicago, Illinois 60607-7059

Darwin ChangNCTS and Physics Department, National Tsing-Hua University, Hsinchu 30043, Taiwan, Republic of China

and Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309

Wai-Yee KeungPhysics Department, University of Illinois at Chicago, Chicago, Illinois 60607-7059

~Received 20 December 2000; published 8 June 2001!

We investigate a potentially largeCP violating asymmetry in the decay of a neutral scalar or pseudoscalar

Higgs boson into at t pair. The source of theCP nonconservation is the complex mixing in the top squarkt L,R

sector. One of the interesting consequences is the different rates of the Higgs boson decays intoCP conjugatepolarized states.

DOI: 10.1103/PhysRevD.64.015010 PACS number~s!: 14.80.Cp, 11.30.Er, 13.88.1e, 14.80.Ly

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I. INTRODUCTION

The standard model~SM! of particle interactions containoneCP violating parameter, which is a complex phase in tquark sector of the SM. This phase appearing in the qumixing matrix of the charged current is expected to acco

for the observedCP violations inK-K mixing, in K decays,

as well as in the potentialCP violation in theB-B system.However, it is generally believed that new physics beyo

the SM must exist. One of the major motivations for this isunderstand the seemingly unnaturalness of the Higgs bomass at the electroweak scale in the SM, the so-called gahierarchy problem. In addition, because of the difficultiesthe SM to account for the baryon asymmetry of the univeas well as to resolve the strongCP problem, it is widelyaccepted that new sources ofCP violation are needed. Themost popular extension of the SM that addresses the hiechy problem is the supersymmetric~SUSY! standard mode@1,2#. The extension has many more new~super!particles andparameters compared to the SM. With all these new pareters, there are many possible new sources forCP violation.The phenomenology ofCP violation caused by these nesources is rich and diverse. The effect of these new souof CP violation may surface in the data before any supparticle is discovered.

Even in the minimal supersymmetric standard mo~MSSM!, which only augments superpartners of known pticles in the SM, the Higgs sector contains new sourcesCP violation in its couplings to superparticles. When themterm in the Higgs superpotential and the soft-SUSY-breakA terms are complex, the triboson couplings betweenHiggs bosons and the squarks can containCP violation. Inthe MSSM with the simplest universal soft supersymme

0556-2821/2001/64~1!/015010~8!/$20.00 64 0150

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breaking @3#, there are two newCP violating couplingswhich can be defined to be the phases ofm andA terms in aconvention that makes the others new couplings real. Thfore, these new sources ofCP violation are generic to allsupersymmetric theories. In addition, they also have bused as one of the leading sources ofCP violation in ascheme to use MSSM to generate baryon number asymmof the Universe in electroweak phase transition@4#. There-fore, it should be important to look for collider phenomenoogy that can check these mechanism. For example, thcomplex couplings lead to a complex phase in the mixing@5#of top squark states. It is the purpose of this paper to invtigate one consequence of thisCP violating source in collid-ers.

It is expected that the future colliders are able to produCP violation signals@6,7,9,10# in the sectors of heavy particles. In this article we study theCP asymmetry in theHiggs decay into top squark pairs because the largequark or top squark coupling to the Higgs particles can pduce largest effect.

In MSSM, even with soft breaking terms andR symmetrybreaking terms, there is no tree level mixing betweenscalar and the pseudoscalar bosons. Therefore their coupcan be discussed separately. However, the scalar andpseudoscalar bosons mix at one loop, and their effect habe taken into account as we will show later.

II. TOP SQUARK MIXING

The source ofCP violation that we investigate here is duto the mixing in the top squark mass matrix. We useconvention adopted in Ref.@8#. The mass matrix for the topsquarks in the left-right basis is given as

M t25S mQ

2 1mt21D t L

mZ2 cos 2b 2mt~m cotb1At* !

2mt~m* cotb1At! mU2 1mt

21D t RmZ

2 cos 2b D , ~1!

©2001 The American Physical Society10-1

t

is

th

p-

by

FRED BROWNING, DARWIN CHANG, AND WAI-YEE KEUNG PHYSICAL REVIEW D64 015010

whereD t L5 1

2 2 23 sin2 uW andD t R

52 23 sin2 uW. The complex

phased of the off-diagonal elements is the source ofCPviolation:

m* cotb1At5um* cotb1Atueid. ~2!

The top squark mass eigenstates,t 1 , t 2, are related to the lefand right top squark states by an unitary mixing matrix

S t L

t RD 5S 1 0

0 eidD S cosu sinu

2sinu cosu D S t 1

t 2D 5US t 1

t 2D . ~3!

The masses of these eigenstates are given by

m1,22 5 1

2 ~mQ2 1mU

2 12mt21~ 1

2 2 43 sin2 uW!mZ

2 cos 2b7AR!,~4!

R5S mQ2 2mU

2 11

2mZ

2 cos 2b D 2

14mt2um cotb1At* u2.

~5!

Here we denotet 1 as the lighter state. The mixing anglegiven as

tanu52@mQ

2 2mU2 1 1

2 mz2cos 2b1AR#

2mtum cotb1At* u. ~6!

Strong gluino couplings to tops squarks and top quarks inleft-right basis is given by

Lg52A2gst Rg t R2A2gst Lg t L . ~7!

In terms of mass eigenstates

in

ve

01501

e

Lg52A2gst ~PR cosu2PL sinueid! t 1g

2A2gst ~PR sinu1PL cosueid! t 2g, ~8!

wherePL is the left projection12 (12g5) andPR is the right

projection 12 (11g5). We also need the top-squark–to

squark coupling toZ:

LZ52g

cosuW@~ 1

2 2 23 sin2 uW! t L

†i ]mJ t L

2 23 sin2 uWt R

† i ]mJ t R#Zm . ~9!

After mixing, the Lagrangian for theZ coupling in thet 1 , t 2basis is

LZ52g

cosuW@~ 1

2 cos2 u2 23 sin2 uW! t 1

†i ]mJ t 1

1~ 12 sin2 u2 2

3 sin2 uW! t 2†i ]mJ t 21 1

4 sin~2u!

3~ t 1†i ]mJ t 21 t 2

†i ]mJ t 1!#Zm . ~10!

Note that the last term is real in this phase convention.

III. THE HIGGS COUPLINGS TO TOP SQUARKS

In MSSM, there is only one pseudoscalar bosonA0. Thepseudoscalar Higgs coupling to the top squarks is giventhe Lagrangian

LA5~ t 1† t 2

†!TAS t 1

t 2D •A0. ~11!

The matrixTA is given as

TA5mt

v2S 2 sinu cosu Im~A! 2 i ~cos2 uA* 1sin2 uA!

i ~cos2 uA1sin2 uA* ! 22 sinu cosu Im~A!D , ~12!

lar

n-

an

avyis

and A is defined asA5(At cosb2m* sinb)e2id. Note thatthe nonvanishing ofT11

A or T22A is a sure sign ofCP violation

already~similar toKL→2p). However, if for some reasonmand At happen to have the same phase,T11

A and T22A will

vanish because in this very special case the phase in thesquark mass matrix and that in the pseudoscalar couplcan be removed simultaneously.

The pseudoscalar Higgs coupling to the top quark is giby the following Lagrangian:

L AY5

gmt

2mWcotb t ig5tA0. ~13!

topgs

n

The neutral scalar Higgs sector is made up two scaeigenstateH0 andh0. There masses are given as

mH,h2 5 1

2 @mA21mZ

26A~mA21mZ

2!224mA2mZ

2 cos 2b#.~14!

Since in MSSM the constraint on the lightest scalarh is suchthat it is too light to decay into the top pair, we shall cocentrate on the decay of the heavy Higgs bosonH, which candecay into the top quark pair. Our general framework calso be used for the decay of the lighter bosonh, of course, iffor any reason that it should be heavy enough. The heHiggs coupling to the top squarks in the left-right basisgiven as

0-2

T0H5

2gmZ

cosuWD t L

cos~a1b!2gmt

2 sina

mW sinb

gmt

2 sinb~At* sina1m cosa!

2 , ~15!

CP ASYMMETRY IN THE HIGGS BOSON DECAY INTO . . . PHYSICAL REVIEW D 64 015010

S gmt

2 sinb~At sina1m* cosa! 2

gmZ

cosuWD t R

cos~a1b!2gmt sina

mW sinb

D
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i-ee

doth

d

fis

ht

ing

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rst

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1r.

thesone

where the mixing anglea is given in Ref.@2#. This matrixmust then be transformed into the top squark mass eigstates. This is accomplished by using the top squark mixmatrix

TH5U†T0HU. ~16!

Its Yukawa coupling is

L HY5

gmt sina

2mW sinbt tH0. ~17!

IV. HELICITY CALCULATION OF THE MATRIXELEMENT

To get nonzeroCP asymmetry in Higgs decays, in addtion to CP violating couplings, it is necessary to get thabsorptive parts from the decay amplitudes in order to ovcome the constraint from theCPT theorem. We labeledSI

andPI as the absorptive form factors of the Higgs or pseuHiggs couplings to the top quark. They begin to appear atone-loop level, unlike their dispersive partsS and P, whichcan exist at the tree level

M5u~p!@~S1 iSI !11 i ~P1 iPI !g5#v~p8!. ~18!

In the Weyl representation, theg matrices are given by

g55S 21 0

0 1D , g05S 0 1

1 0D .

The free spinors of momentap,p8 and helicitiesl,l8 aregiven by

u~p,l!5S v2lx1l

v1lx1lD , v~p8,l!5S 2l8v1l8x2l8

l8v2l8x2l8D ,

where thex ’s are two component spinor eigenfunctionssW

• p xl(p)5l xl . The v6 are functions of the energy anmomentum of the particles,v65AE6upu. Notice that thehelicities oft t must matchl85l because of conservation oangular momentum. Our normalization of the spinorul

†ul5vl†vl52E. The asymmetry between the left and rig

matrix elements is given by

A5uM LLu22uM RRu2

uM LLu21uM RRu2. ~19!

The matrix elements are given by

01501

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r-

-e

MLL5As@2b t~S1 iSI !2 i ~P1 iPI !#, ~20!

MRR5As@2b t~S1 iSI !1 i ~P1 iPI !#, ~21!

with b t5(124mt2/s)1/2 ands5mH

2 . The asymmetry can fi-nally be obtained using the definition from Eq.~19!,

A52b t~PSI2PIS!

PI21P21b t2S21b t

2SI2. ~22!

Since we assume the Higgs boson has definiteCP parity atthe tree level, the final state interactions due to exchanggluons or gauge bosons in Ref.@6# are not able to producethis CP asymmetry at the one-loop level. However, the riCP phases in the sector of SUSY partners, especiallygluino and the top squark, can give rise to largeA. For scalarboson decay, the second termPIS in A gives the leadingcontribution; while for pseudoscalar boson decay, the fiterm, PSI is the leading contribution.

The polarization asymmetry is Eq.~22! can be translatedinto the lepton energy asymmetry@6,11,12# in the final semi-leptonic channelt→bl1n. The energyE0( l 1) distribution ofa statict quark decayt→ l 1nb is very simple in the narrowwidth GW approximation whenmb is negligible:

f ~x0!5H x0~12x0!/D if mW2 /mt

2,x,1,

0 otherwise.~23!

Here we denote the scaling variablex052E0( l 1)/mt and thenormalization factor D5 1

6 2 12 (mW /mt)

41 13 (mW /mt)

6.When thet quark is not static, but moves at a speedb t withhelicity L or R, the distribution expression becomes a convlution

f R,L~x,b t!5Ex/(11b t)

x/(12b t)

f ~x0!b tx06~x2x0!

2x02b t

2 dx0. ~24!

Here x52E( l 1)/Et . The kernel above is related to the (6 cosc) polar angular distribution. Similar distributions fothe t decay is related byCP conjugation at the tree-levelUsing the polarization asymmetry formula in Eq.~22!, wecan derive expressions for the energy distributions ofl 2 andl 1:

N21dN/dx~ l 6!5 12 ~16A! f L~x,b t!1 1

2 ~17A! f R~x,b t!.~25!

Here distributions are compared at the same energy forlepton and the antilepton at the rest frame of the Higgs box( l 2)5x( l 1)5x54E( l 6)/MH . To prepare a large sampl

0-3

o

in

-


for analysis, we only require that each event has at leastprompt antileptonl 1 from the t decayor one prompt leptonl 2 from the t decay.

V. ABSORPTIVE PARTS OF 3-POINT VERTICES

We first study the triangle diagram via gluino exchangeFig. 1.

A. The M11 top squark loop

When the intermediate state ist 1 t 1, the Feynman rulegives

:

01501

neiM115~2 iA2gs!

2E N11

i

k22m12

i

k822m12

d4q

~2p!4iT11CF ,

~26!

whereN11 is defined as

N115u~p!~PR cosu2PL sinueid!i ~q”1mg!

q22mg2

3~PL cosu2PR sinue2 id!v~p8!. ~27!

The color factorCF is 43 . The absorptive part of the ampli

tude which is needed forCP violation is obtained by cuttingacross the momentumsk and k8. The discontinuity@13# ofthe matrix element is

Disc~ iM11!5gs

2T11

8pb1CFE u~p!

q” ~12g5 cos 2u!1mg sin~2u!~2cosd1 ig5 sind!

q22mg2 v~p8!

dVk

4p. ~28!

ndl to

isela-

te

The phase space integration involves the following forms

Ji j [sE 1

q22mg2

d Vk

4p.

51

b tb i jlnS b t

21b i j2 22b tb i j 14mg

2/s

b t21b i j

2 12b tb i j 14mg2/s

D , ~29!

sE qm

q22mg2

dVk

4p52Hi j ~p2p8!m1Ki j ~p1p8!m.

~30!

Multiplying both sides by (p2p8)m the Hi j function can beisolated out because (p1p8)•(p2p8) is zero. TheHi j func-tion for any intermediate massmi andmj is

b t2Hi j 511 1

4 ~b i j2 2b t

214mg2/s!Ji j . ~31!

The b i j function is given by

b i j 5A122~mi21mj

2!/s1~mi22mj

2!2/s2. ~32!

Notice that wheni 5 j , b i j reduces tob i5A124mi2/s. The

functionKi j is obtained by contracting Eq.~30! with p1p8:

FIG. 1. Triangle diagram via gluino exchange.

Ki j 52 12 Ji j ~mi

22mj2!/s. ~33!

Notice that for matrix elements with both the top squark athe anti-top-squark of the same type, the term proportiona(p1p8) in Eq. ~30! does not contribute.

After this, the imaginary part of the matrix elementneeded. The imaginary parts are obtained by using the rtion

Disc~M!52i u~p!@SI11PIig5#v~p8!. ~34!

S11I 5

gs2T11b1

16psCF@1mgJ11 sin~2u!cosd12mtH11#,

P11I 5

gs2T11b1

16psCF@2mgJ11 sin~2u!sind#. ~35!

B. The M22 top-squark loop

Similarly, we obtain results for the intermediate sta

t 2 t 2. The matrix element is given by

iM225~2 iA2gs!2E N 22

i

k22m22

i

k822m22

d4q

~2p!4iT22CF ,

~36!

whereN22 is given by

0-4

e

a

n-

ix

yld-x

hef

on


N225u~p!~PR sinu1PL cosueid!i ~q”1mg!

q22mg2

3~PL sinu1PR cosue2 id!v~p8!. ~37!

After integrating the phase space of the intermediate statthe cut diagram, the form factors are

S22I 5

gs2T22b2

16psCF@2mgJ22 sin~2u!cosd12mtH22#,

P22I 5

gs2T22b2

16psCF@1mgJ22 sin~2u!sind#. ~38!

C. The M12 top-squark loop

The amplitude involving the intermediate statet 1 t 2 isgiven by

iM1252i 6gs2T12CFE N 12

1

k22m12

1

k822m22

d4q

~2p!4,

N125u~p!~PR cosu2PL sinueid!~q”1mg!

q22mg2 ~PL sinu

1PR cosue2 id!v~p8!. ~39!

For t 2 t 1, it is

iM2152i 6gs2T21CFE N 21

1

k22m22

1

k822m12

d4q

~2p!4,

N215u~p!~PR sinu1PL cosueid!~q”1mg!

q22mg2 ~PLcosu

2PR sinue2 id!v~p8!. ~40!

After integrating over the intermediate phase space, weup the absorptive parts to give

S12121I 52

gs2b12

8psCF Re@mgT21~cos2 ueid

2sin2 ue2 id!#J12, ~41!

P12121I 52

gs2b12

8psCF Im@2mgT21~sin2 ue2 id

1cos2 ueid!1mt sin~2u!T21~m22

2m12!/s#J12. ~42!

VI. ABSORPTIVE PARTS OF TWO-POINT VERTICES

We study the bubble loops which involve only thetD t pair.

01501

in

dd

A. Z diagrams

Z diagrams that containt 1 t 1 or t 2 t 2 are identical to zerobecause of the phase space integration~see Fig. 2!. Thispoint will become obvious from the result of the mixed i

termediate statest 1 t 2 or t 2 t 1. The M12 matrix element isgiven below:

iM125g2T12NC

4 cos2 uW

sin~2u!

3E N Z

1

l 22mZ2

1

k22m12

1

k822m22

d4k

~2p!4,

whereNZ is given as

NZ5u~p!gm~ 14 2 2

3 sin2 uW2 14 g5!v~p8!~gmn2 l ml n /mZ

2!

3~k2k8!n . ~43!

TheM21 matrix element is very similar to the above matrelement, with the substitution ofT12 by T12* ,

P12121;ZI 5

g2NC

64p

mtb12 sin~2u!

mZ2 cos2uW

m122m2

2

sIm~T12!, ~44!

where the color factorNC53. This graph will contributeonly to CP violation of the scalar Higgs decay. One mathink that without gluino couplings in the graph, one shoube able to rotate away theCP violating phase in scalar coupling T12

H . However, such rotation will produce a comple

phase int 1† t 2Z coupling in Eq.~10!.

B. A0-H 0 mixing

The top squark bubble loop inducesA0-H0 mixing ~seeFig. 3!. We study its absorptive part which contributes to tCP violation. In the heavy Higgs boson mass limit oMSSM, mA0 andmH0 are quite close to each other based

FIG. 2. Z exchange diagram.

FIG. 3. Higgs mixing diagram.

0-5

vey

o-ingair,


the tree-level mass relation in Eq.~14!. However, it is knownthat there is a large higher order correction to the tree-lemass relation. Thus in our following study we allow thmassesmA0 andmH0 to vary independently, not restricted b

g

rte

rv

te

01501

elthe tree-level formula. The matrix element for the pseudscalar Higgs turning into a top squark pair, then becomthe heavy Higgs boson, and finally decaying into a top pis given as

M5igmt sina

2mW sinbu~p!v~p8!(

i jE Tji

H0

mA02

2mH2

Ti jA0

S l

21qD 2

2mi2

id4q/~2p!4

S l

22qD 2

2mj2

. ~45!

aseadchuino

of

uark

ate

sg

lingcted

Making the same cut as that in theZ loop digram, we obtainthe imaginary part of the form factor:

SI~A0→H0→ t t !52gmt

32pmW

sina

sinb(i j

b i j

TjiH0

Ti jA0

mA02

2mH02 .

~46!

A similar expression is derived for the heavy scalar Higdecay

PI~H0→A0→ t t !52gmt

32pmWcotb(

i jb i j

TjiH0

Ti jA0

mH02

2mA02 .

~47!

VII. PHYSICAL AND NUMERICAL ANALYSES

Before we plunge into the numerical analysis, it is inteesting to check the limit in which the two top squark staare accidentally degenerate. In that case, (M t

2)125(M t2)21

50, (M t2)115(M t

2)22. Therefore m* cotb1At50, andm* andAt should have the same phase which can still seas the source ofCP violation. In that case,u andd in U inEqs.~3!,~12!,~16! and in the definition ofA, should be set tozero.

Thus in this limit, the top squark loops do not contribu

FIG. 4. Light top squark massm1 versus tanb for the casemQ5mU5250,300,350 GeV, m5500 GeV, At5500eip/4 GeV.Horizontal line shows current LEP limit.

s

-s

e

to M11 and M22 in the pseudoscalar case, becauseT11A

5T22A 50. However they still give rise toCP violation in

M12, M21 becauseT12A 5(2 imt /v2)(At* cosb2m sinb).

One may attempt to absorb this phase by rotating the phof, say, the right top squark; however such rotation will leto complex gluino-top-quark–top-squark couplings whicannot be rotated away because of the nonvanishing glmass. From this, it is easy to understand why a factorgluino mass has to appear in Eq.~41! for S12121

I . Similarly,for the scalar Higgs boson decay in the degenerate top sqlimit, the top squark loops still produce noCP violatingeffect in M11andM22, because sinu50 and only the termproportional to the gluino mass inP12121

I contributes as re-flected in Eq.~42!.

It is also straightforward to note that in the degenerlimit, the contributions of bothH0-Z0 and A0-H0 bubblegraphs vanish. In theH0-Z0 case, the phase of the Higgscalar,H, coupling as well as that of the top squark mixincan be rotated away simultaneously~into the gluino cou-plings! without affecting theZ coupling and this is reflectedin m1

22m2250 factor in Eq.~44!. For A0-H0, the phase of

pseudoscalar coupling as well as that of the scalar coupcan be rotated away simultaneously also and this is reflein

(i j

b i j TjiH0

Ti jA0

5b12~T21H0

T12A0

1T21H0

T12A0

!50,

FIG. 5. Light top squark massm1 versus tanb for the case

mQ5mU5300 GeV, f50,14 p, 1

2 p, m5500 GeV, At5500eif

GeV. Horizontal line shows current LEP limit.

0-6

ea

abl

rso

t

eeorfd

g

theor-res-

a

cursre-

the

thede-etom

P


in this particular limit.To illustrate our result numerically, in the following, w

set the parameters so that only the lighter top pair squ

t 1 t 1 are light enough to be on-shell for simplicity. In suchscenario, only some of the above contributions are availaIn Figs. 4 and 5, we show the massm1 of the lightest topsquark versus tanb for different choices of mass parameteand the phase. The best current limit of the lowest boundlightest top squark mass from the CERNe1e2 collider LEPis about 95 GeV@14#. The limit places a nontrivial constrainon tanb, mQ , mU , m, andA through Eqs.~4!,~5!. For ex-ample, for typical MSSM parametersmQ5mU5300 GeV,m5500 GeV,At5500eif GeV, the LEP limit onm1 disfa-vors a low value of tanb&3 for the phasef&p/4. There-fore we set the range of tanb of our study from tanb53 totanb55. A larger tanb is less interesting because thbranching fractions ofA0 or H0 to the top quark pair becomtoo small for theCP asymmetry to be detected. Note that fchosen values ofMQ ,MU , m and a given absolute value oAt , the current limit on the lightest top squark can alreaput a nontrivial constraint on theCP violating phasef. Ifone wishes to study the possibility of a much heavier Hig

FIG. 6. Asymmetry of pseudoscalar Higgs decaymQ5300 Gev,

mU5300 GeV,m5500 GeV,At5500eip4 GeV, mA5400 GeV,mH

5420 GeV.

FIG. 7. Asymmetry of pseudoscalar Higgs decay versusm1, formU5mQ , m5500 GeV, At5500eip/4 GeV, mA5400 GeV, mH

5420 GeV.

01501

rk

e.

n

y

s

boson which can decay into all channels of top squarks,contributions of the remaining diagrams can be easily incporated into the numerical analysis using the analytic expsion provided here.

A. Pseudoscalar-Higgs boson decay

In the model of our study, theA0 retains its status aspseudoscalar boson at the tree level.CP violation in thepseudoscalar Higgs boson decay into top quark pairs ocstarting at the one-loop level. The leading contributionquires induced scalar form factorSI which, as we haveshown, can be obtained from the absorptive part due tointermediatetD t state. Notice that there is noZ loop contribu-tion toSI in the Higgs boson decay. Figures 6 and 7 showasymmetry for the pseudoscalar Higgs boson decay asfined by Eq.~22!. Figure 8 shows the branching ratios of thpseudoscalar-Higgs boson decay to top quark pairs, botpairs, and top squark pairs. For small tanb(3 5) the decaychannel is mostly top quark pairs.

FIG. 8. Branching ratios for pseudoscalar Higgs decay,mQ

5300 Gev, mU5300 GeV, m5500 GeV, At5500eip/4 GeV, mA

5400 GeV, mH5420 GeV. Vertical line shows current the LElimit on the top squark mass.

FIG. 9. Asymmetry of heavy Higgs decaymQ5300 Gev,mU

5300 GeV, m5500 GeV, At5500eip/4 GeV, mA5400 GeV, mH

5420 GeV.

0-7

s-sus

g

uca

y.ra ofel,

ce

e

p


B. Higgs decay

In the Higgs decay, theCP violation is caused by termproportional to thePI form factors. TheZ diagrams can contribute in principle if not disallowed by the kinematics. Astated before it does not contribute in our illustration becawe assume a heavyt2. Figures 9 and 10 show theCP asym-metry of the Higgs decay. The branching ratios for the Higto decay into tops, bottoms, top squarks,W’s, and Z’s aregiven in Fig. 11.

VIII. CONCLUSION

The complex mixing among the stop sector can prodCP asymmetry at the level of a few percent in the fin

FIG. 10. Asymmetry of heavy Higgs decay versusm1, for mQ

5mU , m5500 GeV, At5500eip/4 GeV, mA5400 GeV,mH5420 GeV.

,s,

ni

u

01501

e

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products of polarizedt t states from the Higgs boson decaSuch asymmetry can be measured in the energy spectthe final leptons. Unlike the usual two-Higgs-doublet modthe CP violation does not require the mixing amongA0 andH0 states at the tree level.

ACKNOWLEDGMENTS

This work was supported in part by National ScienCouncil of ROC, and by U.S. Department of Energy~GrantNo. DE-FG02-84ER40173!. This work was supported by thDepartment of Energy, Contract DE-AC03-76SF00515.

FIG. 11. Branching ratios for heavy Higgs decaymQ5300 Gev,mU5300 GeV, m5500 GeV, At5500eip/4 GeV, mA5400 GeV,mH5420 GeV. Vertical line shows the current LEP limit on the toquark mass.

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asymmetry in the Higgs boson decay into a top quark pair due to top squark mixing